Quantum Theories of Dilaton Gravity

Abstract

Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the dilaton $\varphi$ and conformal factor $\rho$. A precise connection is given between the constraint that the theory be independent of the background metric and conformal invariance of the resulting sigma model. Although the action is renormalizable, new coupling constants must be specified at each order in perturbation theory in order to determine the quantum theory. These constants may be viewed as initial data for the beta function equations. It is argued that not all choices of this data correspond to physically sensible theories of gravity, and physically motivated constraints on the data are discussed. In particular a recently constructed subclass of initial data which reduces the full quantum theory to a soluble Liouville-like theory has energies unbounded from below and thus is unphysical. Possibilities for modifying this construction so as to avoid this difficulty are briefly discussed.

20 pages (Major additions made, including 5 pages on the relation between conformal invariance and background independence.)

References in corpus (17)

• Evanescent Black Holes
• The Endpoint of Hawking Evaporation
• Are Horned Particles the Climax of Hawking Evaporation?
• Black Hole Evaporation in 1+1 Dimensions
• Liouville Models of Black Hole Evaporation
• Quantum Emission from Two-Dimensional Black Holes
• Quantization of a Theory of 2d Dilaton Gravity
• Evaporation of Two Dimensional Black Holes
• Scalar-Tensor Quantum Gravity in Two Dimensions
• Hawking Radiation and Back-Reaction
• Fadeev-Popov Ghosts and 1+1 Dimensional Black Hole Evaporation
• Black Hole Physics from Liouville Theory
• Quantum Black Holes
• Supersymmetry and Positive Energy in Classical and Quantum Two-Dimensional Dilaton Gravity
• Exactly Solvable Models of 2d Dilaton Quantum Gravity
• Quantum Theory of Dilaton Gravity in 1+1 Dimensions
• Classical and Quantum Considerations of Two-dimensional Gravity

Cited by in corpus (52)

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• Cosmological solutions of supercritical string theory
• Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation
• Numerical Analysis of Black Hole Evaporation
• Supersymmetry and Positive Energy in Classical and Quantum Two-Dimensional Dilaton Gravity
• Finite sigma models and exact string solutions with Minkowski signature metric
• Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter
• Soluble models in 2d dilaton gravity
• A Non-Singular Black Hole
• Exact Operator Quantization of a Model of Two-Dimensional Dilaton Gravity
• Nonsingular Lagrangians for Two Dimensional Black Holes
• Spacetime Embedding Diagrams for Black Holes
• On aspects of 2-dim dilaton gravity, dimensional reduction and holography
• Black hole entropy from classical Liouville theory
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• Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
• Dilaton Quantum Cosmology in Two Dimensions
• Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter
• Conformally Invariant Boundary Conditions for Dilaton Gravity
• Quantum Theory of Dilaton Gravity in 1+1 Dimensions
• A Unified Approach to Solvable Models of Dilaton Gravity in Two-Dimensions Based on Symmetry
• Central charges and boundary fields for two dimensional dilatonic black holes
• Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy
• Sine-Gordon soliton as a model for Hawking radiation of moving black holes and quantum soliton evaporation
• Tachyon Splits the (d = 2 String) Black Hole Horizon and Turns it Singular
• Dilaton Gravity in $2+\epsilon$ Dimensions
• Polymer quantization of CGHS model- I
• White Holes, Black Holes and Cpt in Two Dimensions
• One-loop Effective Action for a Generic 2D Dilaton Gravity Theory
• Toy Models For Black Hole Evaporation
• Two-dimensional quantum black holes: Numerical methods
• Schrödinger evolution of two-dimensional black holes
• Space-time Geometry in Exactly Solvable Quantum Dilaton Gravity
• Black Hole Formation and Space-Time Fluctuations in Two Dimensional Dilaton Gravity and Complementarity
• A theory of quantum black holes: non-perturbative corrections and no-veil conjecture
• N=2 Supersymmetry in Two-Dimensional Dilaton Gravity
• Backreaction Effects in the Two-Dimensional Dilaton Gravity
• Equilibrium Two-Dimensional Dilatonic Spacetimes
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• A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix
• Hadamard Renormalization of a 2-Dimensional Dirac Field
• Quantum Aspects of Black Holes
• The No-Hair Conjecture in 2D Dilaton Supergravity
• Quantized 2d Dilaton Gravity and Black Holes
• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Black Hole Uncertainties
• All Or Nothing: On the Small Fluctuations of Two-Dimensional String-Theoretic Black Holes
• Black Hole Physics from Two Dimensional Dilaton Gravity based on $SL(2,R)/U(1)$ Coset Model